package first

/*
	在一个 n * m 的二维数组中，每一行都按照从左到右递增的顺序排序，每一列都按照从上到下递增的顺序排序。请完成一个高效的函数，输入这样的一个二维数组和一个整数，判断数组中是否含有该整数。
	示例:

	现有矩阵 matrix 如下：

	[
	  [1,   4,  7, 11, 15],
	  [2,   5,  8, 12, 19],
	  [3,   6,  9, 16, 22],
	  [10, 13, 14, 17, 24],
	  [18, 21, 23, 26, 30]
	]
	给定 target=5，返回true。

	给定target=20，返回false。

	限制：

	0 <= n <= 1000

	0 <= m <= 1000

	来源：力扣（LeetCode）
	链接：https://leetcode-cn.com/problems/er-wei-shu-zu-zhong-de-cha-zhao-lcof
	著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。
*/
func FindNumberIn2DArray(matrix [][]int, target int) bool {
	return findNumberIn2DArray(matrix, target)
}
func findNumberIn2DArray(matrix [][]int, target int) bool {
	if len(matrix) == 0 {
		return false
	}
	// mid_row, mid_col
	return _findNumberIn2DArray(matrix, target, 0, 0, len(matrix)-1, len(matrix[0])-1)
}

/*
	{1, 2, 3, 4, 5},
	{6, 7, 8, 9, 10},
	{11, 12, 13, 14, 15},
*/
func _findNumberIn2DArray(matrix [][]int, target, start_row, start_col, end_row, end_col int) bool {
	if start_col > end_col || start_row > end_row {
		return false
	}
	mid_row := (start_row + end_row) / 2
	mid_col := (start_col + end_col) / 2
	cur := matrix[mid_row][mid_col]
	if target == cur {
		return true
	}
	if target < cur {
		return _findNumberIn2DArray(matrix, target, start_row, start_col, mid_row-1, end_col) ||
			_findNumberIn2DArray(matrix, target, start_row, start_col, end_row, mid_col-1)
	} else {
		return _findNumberIn2DArray(matrix, target, start_row, mid_col+1, end_row, end_col) ||
			_findNumberIn2DArray(matrix, target, mid_row+1, start_col, end_row, end_col)
	}
}
